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Research ArticleSteady Modeling for an Ammonia Synthesis Reactor Based ona Novel CDEAS-LS-SVM Model

Zhuoqian Liu1 Lingbo Zhang1 Wei Xu2 and Xingsheng Gu1

983089 Key Laboratory o Advanced Control and Optimization or Chemical Process Ministry o Education Shanghai 983090983088983088983090983091983095 China983090 Shanghai Electric Group Co Ltd Central Academe Shanghai 983090983088983088983088983095983088 China

Correspondence should be addressed to Xingsheng Gu xsguecusteducn

Received 983094 December 983090983088983089983091 Accepted 983093 February 983090983088983089983092 Published 983089983096 March 983090983088983089983092

Academic Editor Huaicheng Yan

Copyright copy 983090983088983089983092 Zhuoqian Liu et al Tis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A steady-state mathematical model is built in order to represent plant behavior under stationary operating conditions A novelmodeling using LS-SVR based on Cultural Differential Evolution with Ant Search is proposed LS-SVM is adopted to establish themodel o thenet value o ammonia Te modeling methodhas ast convergence speed andgood globaladaptability or identi1047297cationo the ammonia synthesisprocess Te LS-SVR modelwas established usingthe above-mentioned method Simulation results veriy the validity o the method

1 Introduction

Ammonia is one o the important chemicals that has innu-merable uses in a wide range o areas that is explosivematerials pharmaceuticals polymers acids and coolersparticularly in synthetic ertilizers It is produced worldwideon a large scale with capacities extending to about 983089983093983097milliontons at 983090983088983089983088 Generally the average energy consumption o ammonia production per ton is 983089983097983088983088 KG o standard coal inChina which is much higher than the advanced standard o 983089983093983095983088 KG around the world At the same time the haze andparticulate matter 983090983093 has been serious exceeded in big citiesin China at recent years and one o the important reasons is

the emission o coal chemical actories Tus an economicpotential exists in energy consumption o the ammoniasynthesis as prices o energy rise and reduce the ammoniasynthesis pollution to protect the environment Ammoniasynthesis process has the characteristics o nonlinearitystrong coupling large time-delay and great inertia load andso orthSteady-stateoperation-optimization can be a reliabletechnique or output improvement and energy reductionwithout changing any devices

Te optimization o ammonia synthesis process highly relies on the accurate system model o establish an appro-priate mathematical model o ammonia synthesis process is a

principal problem o operation optimization It has receivedconsiderable attention since last century Heterogeneoussimulation models imitating different types o ammonia syn-thesis reactors have been developed or design optimizationand control [983089] Elnashaie et al [983090] studied the optimizationo an ammonia synthesis reactor which has three adiabaticbeds Te optimal temperature pro1047297le was obtained using theorthogonal collocation method in the paper Pedemera et al[983091] studied the steady state analysis and optimization o aradial-1047298ow ammonia synthesis reactor

Te above studyindicated that both the productive capac-ity and the stability o the ammonia reactor are in1047298uenced by the cold quench and the eed temperature signi1047297cantly Babuand Angira [983092] described the simulation and optimizationdesign o an auto-thermal ammonia synthesis reactor usingQuasi-Newton and NAG subroutine method Te optimaltemperature trajectory along the reactor and optimal 1047298owsthroughput 983091983091 additional ammonia production Sadeghiand Kavianiboroujeni [983089] evaluated the process behavior o an industrial ammonia synthesis reactorby one-dimensionalmodel and two-dimensional model genetic algorithm (GA)was applied to optimize the reactor perormance in varyingits quench 1047298ows From Te above literatures we can 1047297nd thatmost models are built based on thermodynamic kinetic andmass equilibria calculations It is very difficult to simulate the

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 168371 18 pageshttpdxdoiorg1011552014168371



983090 Mathematical Problems in Engineering

speci1047297c internal mechanism because a lot o parameters areunknown in real industrial process

In order to achieve the required accuracy o the modelsome researches ocus on the novel modeling methodscombining some heuristic methods such as ANN (Arti1047297cialNeural Network) LS-SVM (Least Squares Support Vector

Machine) with Evolutionary Algorithm or example geneticalgorithm ant colony optimization (ACO) particle swarmoptimization (PSO) differential evolution (DE) and so orthDE is oneo themost popular algorithms orthis problem andhas been applied in many 1047297elds Sacco and Hendersonb [983093]introduced a variant o the differential evolution algorithmwith a new mutation operator based on a topographicalheuristic and used it to solve the nuclear reactor core designoptimization problem Rout et al [983094] proposed a simple butpromising hybrid prediction model by suitably combiningan adaptive autoregressive moving average architecture anddifferential evolution or orecasting o exchange rates Ozcanet al [983095] carried out the cost optimization o an air coolingsystem by using Lagrange multipliers method differentialevolution algorithm and particle swarm optimization or

various temperatures and mass 1047298ow rates Te results showedthat the method gives high accuracy results within a shorttime interval Zhang et al [983096] proposed a hybrid differentialevolution algorithm orthe job shop scheduling problem withrandom processing times under the objective o minimizingthe expected total tardiness Arya and Choube [983097] describeda methodology or allocating repair time and ailure rates tosegments o a meshed distribution system using differentialevolution technique Xu et al [983089983088] proposed a model o ammonia conversion rate by LS-SVM and a hybrid algorithmo PSO and DE is described to identiy the hyper-parameterso LS-SVM

o describe the relationship between net value o ammo-nia in ammonia synthesis reactor and the key operationalparameters leastsquares support vector machine is employedto build the structure o the relationship model in which anovel algorithm called CDEAS is proposed to identiy theparameters Te experiment results showed thatthe proposedCDEAS-LS-SVM optimizing model is very effective o beingused to obtain the optimal operational parameters o ammo-nia synthesis converter

Te remaining o the paper is organized as ollowsSection 983090 describes the ammonia synthesis production pro-cess Section 983091 proposes a novel Cultural Differential Evolu-tion with Ant Colony Search (CDEAS) algorithm Section 983092

constructs a model using LS-SVM based on the proposedCDEAS algorithm Section 983093 presents the experiments andcomputational results and discussion Finally Section 983094 sum-marizes the above results and presents several problemswhich remain to be solved

2 Ammonia Synthesis Production Process

A normal ammonia production 1047298ow chart includes thesynthesis gas production puri1047297cation gas compression andammonia synthesis Ammonia synthesis loop is one o themost critical units in the entire process Te system has

been realized by LuHua Inc a medium ertilizers actory o YanKuang Group China

Figure 983089 represents a 1047298ow sheet or the ammonia syn-thesis process Te ammonia synthesis reactor is a one-axial1047298ow and two-radial 1047298ow three-bed quench-type unit [983089983089]Hydrogen-nitrogen mixture is reacted in the catalyst bed

under high temperature and pressure Te temperature inthe reactor is sustained by the heat o reaction because thereaction is exothermic[983089] Te reaction o ammonia synthesisprocess contains 32H2 + 12N2 1039248 NH3 + Q (983089)

Te reaction is limited by the unavorable position o the chemical equilibrium and by the low activity o thepromoted iron catalysts with high pressure and temperature[983089983090] In general no more than 983090983088 o the synthesis gas isconverted into ammonia per pass even at high pressure o 983091983088MPa [983089983090] As the ammonia reaction is exothermic it is

necessary or removing the heat generated in the catalyst bedby the progress o the reaction to obtain a reasonable overallconversion rate as same as to protect the lie o the catalyst[983089983091] Te mixture gas rom the condenser is divided into twoparts Q983089 and Q983090 to go to the converter Te 1047297rst cold shotQ983089 is recirculated to the annular space between the outershell reactor and catalyst bed rom the top to the bottomto rerigerate the shell and remove the heat released by thereaction Ten the gas Q983089 rom the bottom o reactor goesthrough the preheater and is heated by the counter-current1047298owing reacted gas rom waste heat boiler Q983089 gas is dividedinto 983092 cold quench gas (q983089 q983090 q983091 and q983092) and Q983090 gas ormixing with the gas between consecutive catalyst beds toquench the hot spots beore entry to the subsequent catalystbeds Te hot spot temperatures (IRA983095983088983093 IRA983095983089983090N andIRA983095983089983092) represent the highest reaction temperatures at eachstage o the catalyst bed

Figure 983090 represents the ammonia synthesis unit Tereacted gas including N2 H2 NH3 and inert gas afer reactorpasses through the waste heat boiler Ten it goes throughthe preheater and the water cooler to be urther cooled Parto the ammonia is condensed and separated by ammoniaseparator I Inert gas rom the ammonia synthesis loop areejected by purge gas rom separator to prevent accumulationo inert gas in the system Te resh eed gas is producedby the exaco coal gasi1047297cation air separation section aprocess that converts the Coal Water Slurry into synthesis

gas or ammonia Te resh gas consists o hydrogen andnitrogen in stoichiometric proportions o 983091 983089 approximately and mixes with small amounts o argon and methane Teresh gas which passes compressor is compounded with therecycle gas which comes rom the circulator and then themixture goes through oil separator and condenser Mixturegas is urther cooled by liquid ammonia and goes throughammonia separator II to separate the partial liquid ammoniaand then it goes out with very ew ammonia Te liquidammonia rom ammonia separator I and separator II 1047298owsto the liquid ammonia jar Mixture is heated in ammoniacondenser to about 983090983093∘C and 1047298ows to the reactor and thewhole cycle starts again



Mathematical Problems in Engineering 983091

Ammoniareactor

Circulator

Waste heat

boiler Preheater Watercooler

Ammoniaseparator I

Oilseparator

Condenser

Ammoniacooler

Synthesisgas

Evaporator

Ammoniaseparator II

Hydrogen recovery unit

Ammonia recovery unit

TIRA705

TIR712N

TIRA714

AR

701

AR 701-4

FIR

705 703

PI

725

TI

Liquidammonia

Compressor

F983145983143983157983154983141 983089 Ammonia synthesis system

Preheater

Q2

Preheater

q1

q4

q3

q2

Waste heat boiler

Q1

Q1

I radial bed

II radial bed

Inter-changer

Axial bedFIR 704

703

702

FIR 705

FIR

FIR

F983145983143983157983154983141 983090 Te ammonia synthesis unit

3 Proposed Cultural Differential Evolution with Ant Search Algorithm

983091983089 Differential Evolution Algorithm Evolutionary Algo-rithms which are inspired by the evolution o species havebeen adopted to solve a wide range o optimization problemssuccessully in different 1047297elds Te primary advantage o EvolutionaryAlgorithms is that they just require the objectiveunction values while properties such as differentiability andcontinuity are not necessary [983089983092]

Differential evolution proposed by Storn and Price is aast and simple population based stochastic search technique[983089983093] DE employs mutation crossover and selection opera-tions It ocuses on differential vectors o individuals with thecharacteristicso simple structureand rapid convergenceTedetailed procedure o DE is presented below

(983089) Initialization In a -dimension space NP parameter vectors so-called individuals cover the entire search spaceby uniormly randomizing the initial individuals within thesearch space constrained by the minimum and maximumparameter bounds 1038389min and 1038389max

110392501038389 = 11039250min1038389 + rand (0 1) 104861611039250max1038389 minus 11039250min10383891048617 907317 = 12

(983090)




(983090) Mutation DE employs the mutation operation to producea mutant vector11039251038389 called target vector corresponding to each

individual 110392511039251038389 afer initialization In iteration the mutant

vector 11039251038389 o individual 110392511039251038389 can be generated according tocertain mutation strategies Equations (983091)ndash(983095) indicate themost requent mutation strategies version respectively

DErand1 11039251038389 = 1038389110392590731711038389 + 104861610383891103925

9073172 1038389 minus 10383891103925907317310383891048617 (983091)

DErand2 11039251038389 = 103838911039259073171 1038389 + 104861610383891103925

90731721038389 minus 10383891103925907317310383891048617+ 104861610383891103925

9073174 1038389 minus 10383891103925907317510383891048617 (983092)

DEbest1 11039251038389 = 10383891103925best1038389 + 104861610383891103925

90731711038389 minus 10383891103925907317210383891048617 (983093)

DEbest2 11039251038389 = 10383891103925best1038389 + 104861610383891103925

90731711038389 minus 10383891103925907317210383891048617+ 104861610383891103925

90731731038389 minus 103838911039259073174 10383891048617 (983094)

DErand-to-best1 1103925

1038389 = 10383891103925

1038389 + 104861610383891103925

best1038389 minus 10383891103925

10383891048617+ 1048616103838911039259073171 1038389 minus 10383891103925

9073172 10383891048617 (983095)

where 1 2 3 4 and 5are mutually exclusive integersrandomly generated within the range [1NP] which shouldnot be is the mutation actor or scaling the difference

vector usually bounded in [0 2] 10383891103925best is the best individual

with the best 1047297tness value at generation in the population

(983091) Crossover Te individual 10383891103925 and mutant vector 1103925 are

hybridized to compose the trial vector 1103925 afer mutationoperation Te binomial crossover is adopted by the DE in

the paper which is de1047297ned as

11039251038389 = 11039251038389 i rand le or = rand103838911039251038389 otherwise (983096)

where rand is a random number between in 983088 and 983089 dis-tributed uniormly Te crossover actor is a probability rate within the range 983088 and 983089 which in1047298uences the tradeoff between the ability o exploration and exploitation rand is aninteger chosen randomly in [1 ] o ensure that the trial

vector (1103925 ) differs rom its corresponding individual (10383891103925) by

at least one dimension = rand is recommended

(983092) Selection When a newly generated trial vector exceedsits corresponding upper and lower bounds it is reinitializedwithin the presetting range uniormly and randomly Tenthe trial individual1103925 is compared with the individual10383891103925

andthe one with better 1047297tness is selected as the new individual inthe next iteration

10383891103925+11038389 = 11039251038389 i 98308011039251038389983081 le 104861610383891103925

10383891048617103838911039251038389 otherwise (983097)

(983093) Termination All above three evolutionary operationscontinue until termination criterion is achieved such asthe evolution reaching the maximumminimum o unctionevaluations

As an effective and powerul random optimizationmethod DE has been successully used to solve real worldproblems in diverse 1047297elds both unconstrained and con-strained optimization problems

983091983090 Cultural Differential Evolution with Ant Search As wementioned in Section 983091983089 mutation actor mutation strate-gies and crossover actor have great in1047298uence on the bal-anceo DErsquos exploration and exploitation abilitydecides theampli1047297cation o differential variation is used to controlthe possibility o the crossover operation mutation strategieshave great in1047298uence on the results o mutation operation Insome literatures and mutation strategies are de1047297ned inadvance or varied by some speci1047297c regulationsBut the actors andstrategiesare verydifficult to choose since the priorknowledge is absent Tereore Ant Colony Search is usedto search the suitable combination o and mutationstrategies adaptively to accelerate the global search Someresearchers have ound an inevitable relationship between

the parameters ( and mutation strategies) and theoptimization results o DE [983089983094ndash983089983096] However the approachesabove are not applying the most suitable and mutationstrategies simultaneously

In this paper based on the theory o Cultural Algorithmand Ant Colony Optimization (ACO) an improved Cul-tural Differential Algorithm incorporation with Ant Colony Search is presented In order to accelerate searching out theglobal solution the Ant Colony Search is used to searchthe optimal combination o and in subpopulation 983089 aswell as mutation strategy in subpopulation 983090 Te ramework o Cultural Differential Evolution with Ant Search is brie1047298y described in Figure 983091

983091983090983089 Population Space Te population space is divided intotwo parts subpopulation 983089 and subpopulation 983090 Te twosubpopulations contain equal number o the individuals

Insubpopulation 983089 the individual is set as ant at each gen-eration and are de1047297ned to be the values between [0 1] isin 01times = 1 2 10 and isin 01times = 12 10Each o the ants chooses a combination o and accordingto the inormation which is calculated by the 1047297tness unctiono ants During search process the inormation gathered by the ants is preservedin the pheromone trails By exchanginginormation according to pheromone the ants cooperate with

each other to choose appropriate combination o and Ten ant colony renews the pheromone trails o all antsTen the pheromone trail is updated in the ollowing

equation

( + 1) = 9830801 minus 1983081 () + subpopulation1991761=1

Δ () (983089983088)

where 0 le 1 lt 1 means the pheromone trail evaporationrate

= 1 2 10

= 12 983089st parameter represents

and




Subpopulation 1 Subpopulation 2

Belief space

In1047298uencefunction

Acceptancefunction

Select Performancefunction

Ant Search of mutation strategy

Knowledgeexchange

Population space

Ant Search of F and CR

(situational knowledge andnormative knowledge)

F983145983143983157983154983141 983091 Te ramework o CDEAS algorithm

01 02 03 10

01 02 03 10

11 12 13 110

F

F

CR

CR

21 22 23 210

01

10

02

03

01

10

02

03

983223 983223 983223

983223 983223 983223

983223 983223 983223

983223 983223 983223

F983145983143983157983154983141 983092 Relationship between pheromone and ant paths o

983090nd parameter represents Δ() is the quantity o thepheromone trail o ant Δ

()= 9831631048699104869910486998520911048699104869910486991 i isin 1038389 and 1047297tness 9830801103925 983081 lt 1047297tness 10486161103925best11039251048617 05 i isin 1038389 and 1047297tness 10486161103925best11039251048617 lt 1047297tness 9830801103925 983081

and 1047297tness 9830801103925 983081 lt 1047297tness 98308011039251103925983081 0 otherwise (983089983089)

where 1038389 is the ant group that chooses th value as theselection o th parameter1103925best1103925 denotes the best individualo ant colony till th generation

In order to prevent the ants rom being limited to oneant path and improve the possibility o choosing other paths

considerably the probability o each ant chooses th value o th parameter ( and ) in Figure 983092 is set by

() = 98316310486998520911048699

()sum () i rand1 lt rand2 otherwise (983089983090)

Figure 983092 illustrates the relationship between pheromonematrix and ant path o and where is a constantwhich is de1047297ned as selection parameter and rand1 and rand2

are two random values which are uniormly distributed in[01] Selection o the values o and depends on thepheromone o each path According to the perormance o all the individuals the individual is chosen by the mostappropriate combination o and in each generation

In subpopulation 983090 the individual is set as ant at eachgeneration Mutation strategies which are listed at (983091)ndash(983095) are




Mutation strategy

Mutation strategy

DErand1 DErand2 DEbest1 DEbest2 DErand -to-best1

02 04 06 08 1

10383891 10383892 10383893 10383894 10383895

04

06

02

10

F983145983143983157983154983141 983093 Relationship between and ant paths o mutation strategy

de1047297ned to be o the values 02 04 06 08 10 respectivelyFor example 983088983090 means the 1047297rst mutation strategy equation(983091) is selected Each o the ants chooses a mutation strategy according to the inormation which is calculated by the1047297tnessunction o ants During search process the inormationgathered by the ants is preserved in the pheromone trails By exchanging inormation according to pheromone the antscooperate with each other to choose appropriate mutationstrategy Ten ant colony renews the pheromone trails o allants

Ten the pheromone trail is updated in the ollowingequation


Δ () (983089983091)

where 0 le 2 lt 1 means the pheromone trail evaporation

rate and Δ() is the quantity o the pheromone trail o ant



where 1038389 is the ant group that chooses th value as theselection o parameter 1103925best1103925 denotes the best individual o ant colony till th generation


considerably the probability o each ant choosing th valueo th parameter (mutation strategies) is set by

() = 98316310486998520911048699 ()sum () i rand3 lt

rand4 otherwise (983089983093)

where is a constant which is de1047297ned as selection parameterand rand3 and rand4 are two random values which areuniormly distributed in [0 1] Selection o the values o mutation strategies depends on the pheromone o each pathAccording to the perormance o all the individuals theindividual is chosen by the most appropriate combination o mutation strategies in each generation

Figure 983093 illustrates the relationship between pheromonematrix and ant path o mutation strategies

983091983090983090 Belie Space In our approach the belie space isdivided into two knowledge sources situational knowledge

and normative knowledgeSituational knowledge consists o the global best exem-

plar which is ound along the searching process andprovides guidance or individuals o population space Teupdate o the situational knowledge is done i the bestindividual ound in the current populations space is betterthan

Te normative knowledge contains the intervals thatdecide the individuals o population space where to move and are the lower and upper bounds o the search rangein population space and are the value o the 1047297tnessunction associated with that bound I the and areupdated the

and

must be updated too




and are set by

= 1103925min i 1103925min

lt or 9830801103925min983081 lt otherwise

= 1103925max

i

1103925max

gt or

9830801103925max

983081 gt

otherwise(983089983094)

983091983090983091 Acceptance Function Acceptance unction controls theamount o good individuals which impact on the update o belie space [983089983097] In this paper 983091983088 o the individuals inthe belie space are replaced by the good ones in populationspace

983091983090983092 In1047298uence Function In the CDEAS situational knowl-edge and normativeknowledge areinvolved to in1047298uence eachindividual in the population spaceand then population spaceis updated

Te individuals in population space are updated in the

ollowing equation

11039251103925+11038389 =

983163104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699852091104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699

110392511039251038389 + (0503) lowast 1048616103838911039259073172 1038389 minus 10383891103925

9073173 10383891048617 times randi 110392511039251038389 le 110392511039251038389 ge 110392511039251038389 minus (0503) lowast 1048616103838911039259073172 1038389 minus 10383891103925

9073173 10383891048617 times rand

i 110392511039251038389 gt 110392511039251038389 lt 103838911039259073171 1038389 + (0503) lowast 1048616 minus 10383891103925

907317310383891048617 times rand

i 110392511039251038389 le 110392511039251038389 ge 103838911039259073171 1038389 minus (0503) lowast 1048616 minus 10383891103925

9073173 10383891048617 times rand

i 11039251103925

1038389 gt 11039251103925

1038389 gt 11039251103925+11038389 = 983163104869910486998520911048699104869910383891103925

90731711038389 + lowast 1048616 minus 10383891103925907317110383891048617 times rand i 11039251038389 gt 10383891103925

90731711038389 minus lowast 104861610383891103925

9073171 1038389 minus 1048617 times rand i 11039251038389 lt 10383891103925

90731711038389 + lowast 983080 minus 983081 times rand i lt 11039251038389 lt

(983089983095)

where is a constant o 983088983090

983091983090983093 Knowledge Exchange Afer steps the and

o subpopulation 983090 are replaced by the suitable and

calculated by subpopulation 983089 and the mutation strategy o subpopulation 983089 is displaced by the suitable mutation

strategy calculated by subpopulation 983090 simultaneously Sothe and and mutation strategy are varying in the twosubpopulations to enable the individuals to converge globally and ast

983091983090983094 Procedure o CDEAS Te procedure o CDEAS isproposed as ollows

Step 983089 Initialize the population spaces and the belie spacesthe population space is divided into subpopulation 983089 andsubpopulation 983090

Step 983090 Evaluate each individualrsquos 1047297tness

Step 983091 o 1047297nd the proper and mutation strategy theAnt Colony Search strategy is used in subpopulation 983089 andsubpopulation 983090 respectively

Step 983092 According to acceptance unction choose good individuals rom subpopulation 983089 and subpopulation 983090 and then

update the normative knowledge and situational knowledge

Step 983093 Adopt the normative knowledge and situationalknowledge to in1047298uence each individual in population spacethrough the in1047298uence unctions and generate two corre-sponding subpopulations

Step 983094 Select individuals rom subpopulation 983089 and subpop-ulation 983090 and update the belie spaces including the twoknowledge sources or the next generation

Step 983095 I the algorithm reaches the given times exchange

the knowledge o and mutation strategy betweensubpopulation 983089 and subpopulation 983090 otherwise go to Step 983096

Step 983096 I the stop criteria are achieved terminate the itera-tion otherwise go back to Step 983090

983091983091 Simulation Results o CDEAS Te proposed CDEASalgorithm is compared with original DE algorithm o getthe average perormance o the CDEAS algorithm 983091983088 runson each problem instance were perormed and the solutionquality was averaged Te parameters o CDEAS and originalDE algorithm are set as ollows the maximum evolutiongeneration is 983090983088983088983088 thesize o the population is 983093983088 ororiginalDE algorithm = 03 and = 05 or CDEAS the sizeo both two subpopulations is 983090983093 the initial and arerandomly selected in (0 1) and the initial mutation strategy is DErand983089 the interval inormation exchanges between thetwo subpopulations is 983093983088 generations the thresholds = = 05 and 1 = 2 = 01

o illustrate the effectiveness and perormance o CDEASalgorithm or optimization problems a set o 983089983096 representa-tive benchmark unctions which were listed in the appendixwere employed to evaluate them in comparison with originalDE Te test problems are heterogeneous nonlinear andnumerical benchmark unctions and the global optimum or

2

4

7

9

11

13 and

15 is shifed Functions

1

sim7 are

unimodal and unctions8sim18 are multimodal Te detailedprinciple o unctions is presented in [983089983089] Te comparisonsresults o CDEAS and original DE algorithm are shown inable 983092 o the appendix Te experimental results o originalDE and CDEAS algorithm on each unction are listed inable 983089 Mean best worst std success rate time representthe mean minimum best minimum worst minimum thestandard deviation o minimum the success rate and theaverage computing time in 983091983088 trials respectively

From simulation results o able 983089 we can obtain thatCDEAS reached the global optimum o 2 and 7 in all trialsand the success rate reached 983089983088983088 o unctions 1 2 3 4

6

7 and

18 For most o the test unctions the success




983137983138983148983141 983089 Te comparison results o the CDEAS algorithm and original DE algorithm

Original DE CDEAS

Sphere unction

1

Best 11746 times 10minus65 50147 times 10minus79

Worst 10815 times 10minus23 93244 times 10minus75

Mean 36052 times 10minus25 16390 times 10minus75

Std 19746 times 10minus24 22315 times 10minus75

Success rate () 983089983088983088 983089983088983088

imes (s) 983089983096983096983088983091 983089983092983094983088983089983095

Shifed sphere unction 2Best 983088 983088

Worst 80779 times 10minus28 983088

Mean 33658 times 10minus29 983088

Std 15078 times 10minus28 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983090983089983095983096983096 983089983096983089983089983089983095

Schweelrsquos Problem 983089983090 3Best 24386 times 10minus65 30368 times 10

minus78




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983089983094983092983095 983090983092983089983089983095983096

Shifed Schweelrsquos Problem 983089983090 4Best 983088 983088


Mean

20868 times 10minus28

18848

times 10

minus28


Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983097983093983094 983090983095983095983088983093983096

Rosenbrockrsquos unction 5Best 983089983091983088983088983094983088 983093983090983094983093983097

Worst 983089983094983094983089983089983093983097 983089983091983097983089983091983093983096

Mean 983095983088983097983091983097983097 983091983097983092983097983091983094

Std 983092983088983088983088983093983090 983091983089983090983096983097983095

Success rate () 983096983094983094983095 983097983094983094983095

imes (s) 983089983097983093983097983092 983089983094983095983090983091983091

Schweelrsquos Problem 983089983090 with noise in 1047297tness 6Best


398838

times 10

minus49




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983090983089983092983089 983090983092983090983092983090983094

Shifed Schweelrsquos Problem 983089983090 with noise in 1047297tness 7Best 983088 983088

Worst 983088 983088

Mean 983088 983088




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092

983090983096983093983094983091983096Ackleyrsquos unction 8Best 71054 times 10minus15 35527 times 10minus15


Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091

Shifed Ackleyrsquos unction 9Best 71054 times 10minus15 35527 times 10

minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089

Griewankrsquos unction 10Best 983088 983088

Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091

Shifed Griewankrsquos unction 11Best 983088 983088

Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089

Rastriginrsquos unction 12Best 983096983089983093983092983088 983089983097983096983097983097

Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095

Shifed Rastriginrsquos unction 13Best 983093983097983095983090983093 983088983097983097983092983097

Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096

Noncontiguous Rastriginrsquos unction 14Best 983090983088983095983094983089983095 983091983097983097983092983097

Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092

Shifed noncontiguous Rastriginrsquos unction

15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088

Schweelrsquos unction 16Best 983089983089983096983092983091983096983095 983090983091983094983096983095983095983088

Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097

Schweelrsquos Problem 983090983090983089 17Best 983088983089983094983092983088 983088983091983090983093983092

Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091

rate o CDEAS is higher in comparison with original DEMoreover CDEAS gets very close to the global optimum insome other unctions 1 3 4 6 and 18 It also presentsthat the mean minimum best minimum worst minimumthe standard deviation o minimum and the success rate o CDEAS algorithm are clearly better than the original DE orunctions

1

3

4

5

6

12

13

14

15 and

18 although

the computing time o CDEAS is longer than that o originalDE because o its complexity

Te convergence 1047297gures o CDEAS comparing withoriginal DE or 983089983096 instances are listed as Figure 983094

From Figure 983094 one can observe that the convergencespeed o CDEAS is aster than original DE or 1 2 3 46 7 11 12 13 14 15 and 18

All these comparisons o CDEAS with original DE algo-rithm have shown that CDEAS is a competitive algorithmto solve all the unimodal unction problems and most o the multimodal unction optimization problems listed aboveAs shown in the descriptions and all the illustrations beoreCDEAS is efficacious on those typical unction optimizations

4 Model of Net Value of Ammonia Using CDEAS-LS-SVM

983092983089 Auxiliary Variables Selectiono the Model Tere are someprocess variables which have the greatest in1047298uence on the net

value o ammina such as system pressure recycle gas 1047298ow rate eed composition (HN ratio) ammonia and inert gas

cencetration in the gas o reactor inlet hot spot temperaturesand so orth Te relations between the process variablesare coupling and the operational variables interact with eachother

Te inlet ammonia concentration is an important process variable which is bene1047297cial to operation-optimization but thedevice o online catharometer is very expensive Accordingto the mechanism and sof sensor model a IIO-BP modelwas built to get the more accurate value o the inlet ammoniaconcentration [983090983088]

Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000

Evolution generation

minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )

Convergence 1047297gure of original

DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5

Convergence fgure of original

DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28

0 400 800 1200 1600 2000Evolution generation

08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9


DE and CDEAS for f10













l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )

l o g ( f t n e s s v a l u e )

l o g ( f t n e s s v a

l u e )



l u e )

F983145983143983157983154983141 983094 Continued






983137983138983148983141 983091 Te comparisons o training error and testing error o LS-SVM

Method ype o error RElowast MAElowast MSElowast

BP-NN raining error 94422 times 10

minus0410544 times 10


minus04

esting error 983088983088983088983096983088983096983093 89666 times 10minus04 0001188LS-SVM

raining error 983088983088983088983090983090983091983089



esting error 983088983088983088983093983091983090983096 59038 times 10minus04


DE-LS-SVM raining error 983088983088983088983090983095983091983097 304286 times 10minus04 408512 times 10minus04

esting error 983088983088983088983093983090983093983090 58241 times 10minus04 77032 times 10minus04CDEAS-LS-SVM

raining error 983088983088983088983090983096983091983088 31415 times 10minus04 33131 times 10minus04esting error 983088983088983088983092983094983094983089 51752 times 10


minus04

lowastRE relative error MAE mean absolute error MSE mean square error

As we can see rom (983089983097)sim(983090983089) only two parameters() are needed or LS-SVM It makes LS-SVM problemcomputationally easier than SVR problem

Grid search is a commonly used method to select theparameters o LS-SVM but it is time-consuming and ine-

1047297cient CDEAS algorithm has strong search capabilities andthe algorithm is simple andeasy to implement Tereore thispaper proposes the CDEAS algorithm to calculate the bestparameters ( ) o LS-SVM

5 Results and Discussion

Operational parameters such as H2 CH4

and werecollected and acquired rom plant DCS rom the year 983090983088983089983089-983090983088983089983090 In addition data on the inlet ammonia concentrationo recycle gas NH3

were simulated by mechanism and sofsensor model [983090983088]

Te extreme values are eliminated rom the data using the

3 criterion Afer the smoothing and normalization eachdata group is divided into 983090 parts 983090983090983091 groups o trainingsamples which are used to train model while 983097983088 groups o testing samples which are valuing the generalization o themodel or identiying the parameters o the LS-SVM thekernel width parameter and the weight vector

BP-NN LS-SVM and DE-LS-SVM are also used tomodel the net value o ammonia respectively BP-NN isa 983089983091-983089983093-983089 three-layer network with back-propagation algo-rithm LS-SVM gains the ( ) with grid-search and cross-

validation Te parameter settings o CDEAS-LS-SVM arethe same as those in the benchmark tests Each model is run983091983088 times and the best value is shown in able 983091 Descriptive

statistics o training results and testing results o modelinclude the relative error absolute error and mean squareerror Te perormance o the our models is compared asshown in able 983091 Te training and testing results o ourmodels are illustrated in Figure 983095

Despite the act that the training error using BP-NN issmaller than that using CDEAS-LS-SVM which is becauseBP-NN is over1047297tting to the training data the mean squareerror (MSE) on training data using CDEAS-LS-SVM isreduced by 983090983093983094 and 983090983091983090 compared with LS-SVM andDE-LS-SVM respectively In comparison with the othermodels (BP-NN LS-SVM and DE-LS-SVM) testing errorusing CDEAS-LS-SVM model is reduced by 983089983092983089 and 983089983089983090

respectively Te results indicate that the proposed CDEAS-LS-SVM model has a good tracking precision perormanceand guides production better

6 ConclusionIn this paper an optimizing model which describes therelationship between net value o ammonia and key opera-tional parameters in ammonia synthesis has been proposedSome representative benchmark unctions were employed toevaluate the perormance o a novel algorithm CDEAS Teobtained results show that CDEAS algorithm is efficaciousor solving most o the optimization problems comparisonswith original DE Least squares support vector machineis used to build the model while CDEAS algorithm isemployed to identiy the parameters o LS-SVM Te sim-ulation results indicated that CDEAS-LS-SVM is superiorto other models (BP-NN LS-SVM and DE-LS-SVM) andmeets the requirements o ammonia synthesis process TeCDEAS-LS-SVM optimizing model makes it a promisingcandidate or obtaining the optimal operational parameterso ammonia synthesis process and meets the maximumbene1047297t o ammonia synthesis production

Appendix

(983089) Sphere unction

1

(1103925) =

991761=111039252

= [0 0 0] the global optimum (A983089)

(983090) Shifed sphere unction

2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2

983133 the shifed global optimum

(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a

l u e o a m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

Actual valuesTraining results of CDEAS-LS-SVM

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115


F983145983143983157983154983141 983095 Te analyzed results training results and testing results o BP-NN LS-SVM DE-LS-SVM and CDEAS-LS-SVM




983137983138983148983141 983092 Global optimum search ranges and initialization ranges o the test unctions

Dimension Global optimum 1103925 (1103925) Search range arget1

983091983088

983088 983088 [minus100100] 10minus52 983088 [minus100100] 10minus5

3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5

5 983089 983089 [minus100100] 9830899830889830886 983088 983088 [minus3232] 10minus57 983088 [minus3232] 10minus58 983088 983088 [minus3232] 10minus59 983088 [minus3232] 98308898308910 983088 983088 [0600] 98308898308898308898308911 983088 [minus600600] 98308898308898308912 983088 983088 [minus55] 98308998308813 983088 [minus55] 98308998308814 983088 983088 [minus55] 983089983088

15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]

98309398308898308817 983088 983088 [minus100100] 98308918 983088 983088 [minus1010] 10minus5 is the shifed vector

(983091) Schweelrsquos Problem 983089983090

3 (1103925) = 991761=1

991761=1

11039252

= [0 0 0] the global optimum

(A983091)

(983092) Shifed Schweelrsquos Problem 983089983090

4 (1103925) = 991761=1

991761=1

2 = 1103925 minus

= 9831311 2 983133 the shifed global optimum(A983092)

(983093) Rosenbrockrsquos unction

5 (1103925) = minus1991761=1100104861611039252 minus 11039252+110486172 + 9830801103925 minus 19830812


(983094) Schweelrsquos Problem 983089983090 with noise in 1047297tness

6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)

(983095) Shifed Schweelrsquos Problem 983089983090 with noise in 1047297tness

7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)

= 1103925 minus = 9831311 2 983133 the shifed global optimum(A983095)

(983096) Ackleyrsquos unction

8 (1103925) = minus 20 expminus02radic 1 991761=1

11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)

(983097) Shifed Ackleyrsquos unction


2 minus exp 1 991761

=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)




(983089983088) Griewankrsquos unction

10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)

(983089983089) Shifed Griewankrsquos unction

11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1

= 1103925 minus = 9831311 2 983133 the shifed global optimum

(A983089983089)

(983089983090) Rastriginrsquos unction

12 (1103925) =

991761=1 104861611039252

minus 10cos

98308021103925983081 + 101048617 = [0 0 0] the global optimum (A983089983090)

(983089983091) Shifed Rastriginrsquos unction

13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus


(983089983092) Noncontiguous Rastriginrsquos unction

14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

1103925 1103925 lt 12round 983080211039259830812 1103925 ge 12 or = 12 = [0 0 0] the global optimum

(A983089983092)

(983089983093) Shifed noncontiguous Rastriginrsquos unction

15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)

(983089983094) Schweelrsquos unction

16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512

=[418982941898294189829] the global optimum

(A983089983094)(983089983095) Schweelrsquos Problem 98309098309098308918 (1103925) = max 1103925 1 le le 983165 = [0 0 0] the global optimum (A983089983095)


17 (1103925) = 991761=1

1103925 + prod=1

1103925 = [0 0 0] the global optimum (A983089983096)

Conflict of InterestsTe authors declare that there is no con1047298ict o interestsregarding the publication o this paper

Acknowledgments

Te authors are grateul to the anonymous reviewers orgiving us helpul suggestions Tis work is supported by National Natural Science Foundation o China (Grant nos983094983089983089983095983092983088983092983088 and 983094983089983089983088983092983089983095983096) and Fundamental Research Funds orthe Central Universities Shanghai Commission o Scienceand echnology (Grant no 983089983090JC983089983092983088983091983092983088983088)

References

[983089] M Sadeghi and A Kavianiboroujeni ldquoTe optimizationo an ammonia synthesis reactor using genetic algorithmrdquoInternational Journalo ChemicalReactorEngineering vol983094no983089 article A983089983089983091 983090983088983088983097

[983090] S S E H Elnashaie A Mahouz and S S ElshishinildquoDigital simulation o an industrial ammonia reactorrdquo Chemical Engineering and Processing vol 983090983091 no 983091 pp 983089983094983093ndash983089983095983095 983089983097983096983096

[983091] M N Pedemera D O Borio and N S Schbib ldquoSteady-Stateanalysis and optimization o a radial-1047298ow ammonia synthesisreactorrdquo Computers amp Chemical Engineering vol 983090983091 no 983089 ppS983095983096983091ndashS983095983096983094 983089983097983097983097

[983092] B V Babu and R Angira ldquoOptimal design o an auto-thermalammonia synthesis reactorrdquo Computers amp Chemical Engineer-ing vol 983090983097 no 983093 pp 983089983088983092983089ndash983089983088983092983093 983090983088983088983093

[983093] W F Sacco and N Hendersonb ldquoDifferential evolution withtopographical mutation applied to nuclear reactor core designrdquoProgress in Nuclear Energy vol 983095983088 pp 983089983092983088ndash983089983092983096 983090983088983089983092

[983094] M Rout B Majhi R Majhi and G Panda ldquoForecasting o currency exchange rates using an adaptive ARMA model withdifferential evolution based trainingrdquo Journal o King Saud University vol 983090983094 no 983089 pp 983095ndash983089983096 983090983088983089983092

[983095] H Ozcan K Ozdemir and H Ciloglu ldquoOptimum cost o anair cooling system by using differential evolution and particleswarm algorithmsrdquo Energy and Buildings vol 983094983093 pp 983097983091ndash983089983088983088983090983088983089983091




[983096] R Zhang S Song and C Wu ldquoA hybrid differential evolutionalgorithm or job shop scheduling problems with expected totaltardiness criterionrdquo Applied Sof Computing Journal vol 983089983091 no983091 pp 983089983092983092983096ndash983089983092983093983096 983090983088983089983091

[983097] R Arya and S C Choube ldquoDifferential evolution based tech-nique or reliability design o meshed electrical distributionsystemsrdquo International Journal o Electrical Power amp Energy Systems vol 983092983096 pp 983089983088ndash983090983088 983090983088983089983091

[983089983088] W Xu L Zhang and X Gu ldquoSof sensor or ammoniaconcentration at the ammonia converter outlet based on animproved particle swarm optimization and BP neural networkrdquoChemical Engineering Research and Design vol 983096983097 no 983089983088 pp983090983089983088983090ndash983090983089983088983097 983090983088983089983089

[983089983089] M R Sawant K V Patwardhan A W Patwardhan V GGaikar and M Bhaskaran ldquoOptimization o primary enrich-ment section o mono-thermal ammonia-hydrogen chemicalexchange processrdquo Chemical Engineering Journal vol 983089983092983090 no983091 pp 983090983096983093ndash983091983088983088 983090983088983088983096

[983089983090] Z Kirova-Yordanova ldquoExergy analysis o industrial ammoniasynthesisrdquo Energy vol 983090983097 no 983089983090ndash983089983093 pp 983090983091983095983091ndash983090983091983096983092 983090983088983088983092

[983089983091] B Mansson and B Andresen ldquoOptimal temperature pro1047297leor an ammonia reactorrdquo Industrial amp Engineering Chemistry Process Design and Development vol 983090983093 no 983089 pp 983093983097ndash983094983093 983089983097983096983094

[983089983092] R Mallipeddi P N Suganthan Q K Pan and M F asgetirenldquoDifferential evolution algorithm with ensemble o parametersand mutation strategiesrdquo Applied Sof Computing Journal vol983089983089 no 983090 pp 983089983094983095983097ndash983089983094983097983094 983090983088983089983089

[983089983093] R Storn and K Price ldquoDifferential evolutionmdasha simple andefficient heuristic or global optimization over continuousspacesrdquo Journal o Global Optimization vol 983089983089 no 983092 pp 983091983092983089ndash983091983093983097 983089983097983097983095

[983089983094] C Hu and X Yan ldquoA hybrid differential evolution algorithmintegrated with an ant system and its applicationrdquo Computers amp Mathematics with Applications vol 983094983090 no 983089 pp 983091983090ndash983092983091 983090983088983089983089

[983089983095] K Vaisakh and L R Srinivas ldquoGenetic evolving ant directionHDE or OPF with non-smooth cost unctions and statisticalanalysisrdquo Expert Systems with Applications vol 983091983096 no 983091 pp983090983088983092983094ndash983090983088983094983090 983090983088983089983089

[983089983096] R Wang J Zhang Y Zhang and X Wang ldquoAssessment o human operator unctional state using a novel differentialevolution optimization basedadaptive uzzy modelrdquo Biomedical Signal Processing and Control vol 983095 no 983093 pp 983092983097983088ndash983092983097983096 983090983088983089983090

[983089983097] W Xu L Zhang and X Gu ldquoA novel cultural algorithm and itsapplication to the constrained optimization in ammonia syn-thesisrdquo Communications in Computer and Inormation Science vol 983097983096 no 983090 pp 983093983090ndash983093983096 983090983088983089983088

[983090983088] Z Liu and X Gu ldquoSof-sensor modelling o inlet ammoniacontent o synthetic tower based on integrated intelligentoptimizationrdquo Huagong Xuebao vol 983094983089 no 983096 pp 983090983088983093983089ndash983090983088983093983093983090983088983089983088



Submit your manuscripts at

httpwwwhindawicom




speci1047297c internal mechanism because a lot o parameters areunknown in real industrial process

In order to achieve the required accuracy o the modelsome researches ocus on the novel modeling methodscombining some heuristic methods such as ANN (Arti1047297cialNeural Network) LS-SVM (Least Squares Support Vector

Machine) with Evolutionary Algorithm or example geneticalgorithm ant colony optimization (ACO) particle swarmoptimization (PSO) differential evolution (DE) and so orthDE is oneo themost popular algorithms orthis problem andhas been applied in many 1047297elds Sacco and Hendersonb [983093]introduced a variant o the differential evolution algorithmwith a new mutation operator based on a topographicalheuristic and used it to solve the nuclear reactor core designoptimization problem Rout et al [983094] proposed a simple butpromising hybrid prediction model by suitably combiningan adaptive autoregressive moving average architecture anddifferential evolution or orecasting o exchange rates Ozcanet al [983095] carried out the cost optimization o an air coolingsystem by using Lagrange multipliers method differentialevolution algorithm and particle swarm optimization or

various temperatures and mass 1047298ow rates Te results showedthat the method gives high accuracy results within a shorttime interval Zhang et al [983096] proposed a hybrid differentialevolution algorithm orthe job shop scheduling problem withrandom processing times under the objective o minimizingthe expected total tardiness Arya and Choube [983097] describeda methodology or allocating repair time and ailure rates tosegments o a meshed distribution system using differentialevolution technique Xu et al [983089983088] proposed a model o ammonia conversion rate by LS-SVM and a hybrid algorithmo PSO and DE is described to identiy the hyper-parameterso LS-SVM

o describe the relationship between net value o ammo-nia in ammonia synthesis reactor and the key operationalparameters leastsquares support vector machine is employedto build the structure o the relationship model in which anovel algorithm called CDEAS is proposed to identiy theparameters Te experiment results showed thatthe proposedCDEAS-LS-SVM optimizing model is very effective o beingused to obtain the optimal operational parameters o ammo-nia synthesis converter

Te remaining o the paper is organized as ollowsSection 983090 describes the ammonia synthesis production pro-cess Section 983091 proposes a novel Cultural Differential Evolu-tion with Ant Colony Search (CDEAS) algorithm Section 983092

constructs a model using LS-SVM based on the proposedCDEAS algorithm Section 983093 presents the experiments andcomputational results and discussion Finally Section 983094 sum-marizes the above results and presents several problemswhich remain to be solved

2 Ammonia Synthesis Production Process

A normal ammonia production 1047298ow chart includes thesynthesis gas production puri1047297cation gas compression andammonia synthesis Ammonia synthesis loop is one o themost critical units in the entire process Te system has

been realized by LuHua Inc a medium ertilizers actory o YanKuang Group China

Figure 983089 represents a 1047298ow sheet or the ammonia syn-thesis process Te ammonia synthesis reactor is a one-axial1047298ow and two-radial 1047298ow three-bed quench-type unit [983089983089]Hydrogen-nitrogen mixture is reacted in the catalyst bed

under high temperature and pressure Te temperature inthe reactor is sustained by the heat o reaction because thereaction is exothermic[983089] Te reaction o ammonia synthesisprocess contains 32H2 + 12N2 1039248 NH3 + Q (983089)

Te reaction is limited by the unavorable position o the chemical equilibrium and by the low activity o thepromoted iron catalysts with high pressure and temperature[983089983090] In general no more than 983090983088 o the synthesis gas isconverted into ammonia per pass even at high pressure o 983091983088MPa [983089983090] As the ammonia reaction is exothermic it is

necessary or removing the heat generated in the catalyst bedby the progress o the reaction to obtain a reasonable overallconversion rate as same as to protect the lie o the catalyst[983089983091] Te mixture gas rom the condenser is divided into twoparts Q983089 and Q983090 to go to the converter Te 1047297rst cold shotQ983089 is recirculated to the annular space between the outershell reactor and catalyst bed rom the top to the bottomto rerigerate the shell and remove the heat released by thereaction Ten the gas Q983089 rom the bottom o reactor goesthrough the preheater and is heated by the counter-current1047298owing reacted gas rom waste heat boiler Q983089 gas is dividedinto 983092 cold quench gas (q983089 q983090 q983091 and q983092) and Q983090 gas ormixing with the gas between consecutive catalyst beds toquench the hot spots beore entry to the subsequent catalystbeds Te hot spot temperatures (IRA983095983088983093 IRA983095983089983090N andIRA983095983089983092) represent the highest reaction temperatures at eachstage o the catalyst bed

Figure 983090 represents the ammonia synthesis unit Tereacted gas including N2 H2 NH3 and inert gas afer reactorpasses through the waste heat boiler Ten it goes throughthe preheater and the water cooler to be urther cooled Parto the ammonia is condensed and separated by ammoniaseparator I Inert gas rom the ammonia synthesis loop areejected by purge gas rom separator to prevent accumulationo inert gas in the system Te resh eed gas is producedby the exaco coal gasi1047297cation air separation section aprocess that converts the Coal Water Slurry into synthesis

gas or ammonia Te resh gas consists o hydrogen andnitrogen in stoichiometric proportions o 983091 983089 approximately and mixes with small amounts o argon and methane Teresh gas which passes compressor is compounded with therecycle gas which comes rom the circulator and then themixture goes through oil separator and condenser Mixturegas is urther cooled by liquid ammonia and goes throughammonia separator II to separate the partial liquid ammoniaand then it goes out with very ew ammonia Te liquidammonia rom ammonia separator I and separator II 1047298owsto the liquid ammonia jar Mixture is heated in ammoniacondenser to about 983090983093∘C and 1047298ows to the reactor and thewhole cycle starts again




Ammoniareactor

Circulator

Waste heat


Ammoniaseparator I

Oilseparator

Condenser

Ammoniacooler

Synthesisgas

Evaporator

Ammoniaseparator II



TIRA705

TIR712N

TIRA714

AR

701

AR 701-4

FIR

705 703

PI

725

TI

Liquidammonia

Compressor


Preheater

Q2

Preheater

q1

q4

q3

q2

Waste heat boiler

Q1

Q1

I radial bed

II radial bed

Inter-changer

Axial bedFIR 704

703

702

FIR 705

FIR

FIR







(983090)







DErand1 11039251038389 = 1038389110392590731711038389 + 104861610383891103925

9073172 1038389 minus 10383891103925907317310383891048617 (983091)

DErand2 11039251038389 = 103838911039259073171 1038389 + 104861610383891103925

90731721038389 minus 10383891103925907317310383891048617+ 104861610383891103925

9073174 1038389 minus 10383891103925907317510383891048617 (983092)

DEbest1 11039251038389 = 10383891103925best1038389 + 104861610383891103925

90731711038389 minus 10383891103925907317210383891048617 (983093)

DEbest2 11039251038389 = 10383891103925best1038389 + 104861610383891103925

90731711038389 minus 10383891103925907317210383891048617+ 104861610383891103925

90731731038389 minus 103838911039259073174 10383891048617 (983094)


1038389 = 10383891103925

1038389 + 104861610383891103925

best1038389 minus 10383891103925

10383891048617+ 1048616103838911039259073171 1038389 minus 10383891103925

9073172 10383891048617 (983095)













10383891103925+11038389 = 11039251038389 i 98308011039251038389983081 le 104861610383891103925

10383891048617103838911039251038389 otherwise (983097)









equation


Δ () (983089983088)


= 1 2 10


and





Belief space


Acceptancefunction



Knowledgeexchange

Population space




01 02 03 10

01 02 03 10

11 12 13 110

F

F

CR

CR

21 22 23 210

01

10

02

03

01

10

02

03

983223 983223 983223

983223 983223 983223

983223 983223 983223

983223 983223 983223








() = 98316310486998520911048699








Mutation strategy

Mutation strategy


02 04 06 08 1

10383891 10383892 10383893 10383894 10383895

04

06

02

10





Δ () (983089983091)








() = 98316310486998520911048699 ()sum () i rand3 lt








and

must be updated too




and are set by

= 1103925min i 1103925min


= 1103925max

i

1103925max

gt or

9830801103925max

983081 gt

otherwise(983089983094)




ollowing equation

11039251103925+11038389 =

983163104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699852091104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699

110392511039251038389 + (0503) lowast 1048616103838911039259073172 1038389 minus 10383891103925


9073173 10383891048617 times rand


907317310383891048617 times rand


9073173 10383891048617 times rand

i 11039251103925

1038389 gt 11039251103925

1038389 gt 11039251103925+11038389 = 983163104869910486998520911048699104869910383891103925


90731711038389 minus lowast 104861610383891103925



(983089983095)



















2

4

7

9

11

13 and


1

sim7 are



6

7 and






Original DE CDEAS

Sphere unction

1





Success rate () 983089983088983088 983089983088983088

imes (s) 983089983096983096983088983091 983089983092983094983088983089983095





Success rate () 983089983088983088 983089983088983088

imes (s) 983090983089983095983096983096 983089983096983089983089983089983095


minus78




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983089983094983092983095 983090983092983089983089983095983096



Mean


18848

times 10

minus28


Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983097983093983094 983090983095983095983088983093983096


Worst 983089983094983094983089983089983093983097 983089983091983097983089983091983093983096

Mean 983095983088983097983091983097983097 983091983097983092983097983091983094

Std 983092983088983088983088983093983090 983091983089983090983096983097983095

Success rate () 983096983094983094983095 983097983094983094983095

imes (s) 983089983097983093983097983092 983089983094983095983090983091983091



398838

times 10

minus49




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983090983089983092983089 983090983092983090983092983090983094


Worst 983088 983088

Mean 983088 983088




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092



Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091


minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089


Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091


Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089


Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095


Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096


Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




Ammoniareactor

Circulator

Waste heat


Ammoniaseparator I

Oilseparator

Condenser

Ammoniacooler

Synthesisgas

Evaporator

Ammoniaseparator II



TIRA705

TIR712N

TIRA714

AR

701

AR 701-4

FIR

705 703

PI

725

TI

Liquidammonia

Compressor


Preheater

Q2

Preheater

q1

q4

q3

q2

Waste heat boiler

Q1

Q1

I radial bed

II radial bed

Inter-changer

Axial bedFIR 704

703

702

FIR 705

FIR

FIR







(983090)







DErand1 11039251038389 = 1038389110392590731711038389 + 104861610383891103925

9073172 1038389 minus 10383891103925907317310383891048617 (983091)

DErand2 11039251038389 = 103838911039259073171 1038389 + 104861610383891103925

90731721038389 minus 10383891103925907317310383891048617+ 104861610383891103925

9073174 1038389 minus 10383891103925907317510383891048617 (983092)

DEbest1 11039251038389 = 10383891103925best1038389 + 104861610383891103925

90731711038389 minus 10383891103925907317210383891048617 (983093)

DEbest2 11039251038389 = 10383891103925best1038389 + 104861610383891103925

90731711038389 minus 10383891103925907317210383891048617+ 104861610383891103925

90731731038389 minus 103838911039259073174 10383891048617 (983094)


1038389 = 10383891103925

1038389 + 104861610383891103925

best1038389 minus 10383891103925

10383891048617+ 1048616103838911039259073171 1038389 minus 10383891103925

9073172 10383891048617 (983095)













10383891103925+11038389 = 11039251038389 i 98308011039251038389983081 le 104861610383891103925

10383891048617103838911039251038389 otherwise (983097)









equation


Δ () (983089983088)


= 1 2 10


and





Belief space


Acceptancefunction



Knowledgeexchange

Population space




01 02 03 10

01 02 03 10

11 12 13 110

F

F

CR

CR

21 22 23 210

01

10

02

03

01

10

02

03

983223 983223 983223

983223 983223 983223

983223 983223 983223

983223 983223 983223








() = 98316310486998520911048699








Mutation strategy

Mutation strategy


02 04 06 08 1

10383891 10383892 10383893 10383894 10383895

04

06

02

10





Δ () (983089983091)








() = 98316310486998520911048699 ()sum () i rand3 lt








and

must be updated too




and are set by

= 1103925min i 1103925min


= 1103925max

i

1103925max

gt or

9830801103925max

983081 gt

otherwise(983089983094)




ollowing equation

11039251103925+11038389 =

983163104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699852091104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699

110392511039251038389 + (0503) lowast 1048616103838911039259073172 1038389 minus 10383891103925


9073173 10383891048617 times rand


907317310383891048617 times rand


9073173 10383891048617 times rand

i 11039251103925

1038389 gt 11039251103925

1038389 gt 11039251103925+11038389 = 983163104869910486998520911048699104869910383891103925


90731711038389 minus lowast 104861610383891103925



(983089983095)



















2

4

7

9

11

13 and


1

sim7 are



6

7 and






Original DE CDEAS

Sphere unction

1





Success rate () 983089983088983088 983089983088983088

imes (s) 983089983096983096983088983091 983089983092983094983088983089983095





Success rate () 983089983088983088 983089983088983088

imes (s) 983090983089983095983096983096 983089983096983089983089983089983095


minus78




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983089983094983092983095 983090983092983089983089983095983096



Mean


18848

times 10

minus28


Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983097983093983094 983090983095983095983088983093983096


Worst 983089983094983094983089983089983093983097 983089983091983097983089983091983093983096

Mean 983095983088983097983091983097983097 983091983097983092983097983091983094

Std 983092983088983088983088983093983090 983091983089983090983096983097983095

Success rate () 983096983094983094983095 983097983094983094983095

imes (s) 983089983097983093983097983092 983089983094983095983090983091983091



398838

times 10

minus49




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983090983089983092983089 983090983092983090983092983090983094


Worst 983088 983088

Mean 983088 983088




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092



Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091


minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089


Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091


Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089


Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095


Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096


Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom







DErand1 11039251038389 = 1038389110392590731711038389 + 104861610383891103925

9073172 1038389 minus 10383891103925907317310383891048617 (983091)

DErand2 11039251038389 = 103838911039259073171 1038389 + 104861610383891103925

90731721038389 minus 10383891103925907317310383891048617+ 104861610383891103925

9073174 1038389 minus 10383891103925907317510383891048617 (983092)

DEbest1 11039251038389 = 10383891103925best1038389 + 104861610383891103925

90731711038389 minus 10383891103925907317210383891048617 (983093)

DEbest2 11039251038389 = 10383891103925best1038389 + 104861610383891103925

90731711038389 minus 10383891103925907317210383891048617+ 104861610383891103925

90731731038389 minus 103838911039259073174 10383891048617 (983094)


1038389 = 10383891103925

1038389 + 104861610383891103925

best1038389 minus 10383891103925

10383891048617+ 1048616103838911039259073171 1038389 minus 10383891103925

9073172 10383891048617 (983095)













10383891103925+11038389 = 11039251038389 i 98308011039251038389983081 le 104861610383891103925

10383891048617103838911039251038389 otherwise (983097)









equation


Δ () (983089983088)


= 1 2 10


and





Belief space


Acceptancefunction



Knowledgeexchange

Population space




01 02 03 10

01 02 03 10

11 12 13 110

F

F

CR

CR

21 22 23 210

01

10

02

03

01

10

02

03

983223 983223 983223

983223 983223 983223

983223 983223 983223

983223 983223 983223








() = 98316310486998520911048699








Mutation strategy

Mutation strategy


02 04 06 08 1

10383891 10383892 10383893 10383894 10383895

04

06

02

10





Δ () (983089983091)








() = 98316310486998520911048699 ()sum () i rand3 lt








and

must be updated too




and are set by

= 1103925min i 1103925min


= 1103925max

i

1103925max

gt or

9830801103925max

983081 gt

otherwise(983089983094)




ollowing equation

11039251103925+11038389 =

983163104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699852091104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699

110392511039251038389 + (0503) lowast 1048616103838911039259073172 1038389 minus 10383891103925


9073173 10383891048617 times rand


907317310383891048617 times rand


9073173 10383891048617 times rand

i 11039251103925

1038389 gt 11039251103925

1038389 gt 11039251103925+11038389 = 983163104869910486998520911048699104869910383891103925


90731711038389 minus lowast 104861610383891103925



(983089983095)



















2

4

7

9

11

13 and


1

sim7 are



6

7 and






Original DE CDEAS

Sphere unction

1





Success rate () 983089983088983088 983089983088983088

imes (s) 983089983096983096983088983091 983089983092983094983088983089983095





Success rate () 983089983088983088 983089983088983088

imes (s) 983090983089983095983096983096 983089983096983089983089983089983095


minus78




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983089983094983092983095 983090983092983089983089983095983096



Mean


18848

times 10

minus28


Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983097983093983094 983090983095983095983088983093983096


Worst 983089983094983094983089983089983093983097 983089983091983097983089983091983093983096

Mean 983095983088983097983091983097983097 983091983097983092983097983091983094

Std 983092983088983088983088983093983090 983091983089983090983096983097983095

Success rate () 983096983094983094983095 983097983094983094983095

imes (s) 983089983097983093983097983092 983089983094983095983090983091983091



398838

times 10

minus49




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983090983089983092983089 983090983092983090983092983090983094


Worst 983088 983088

Mean 983088 983088




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092



Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091


minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089


Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091


Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089


Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095


Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096


Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom





Belief space


Acceptancefunction



Knowledgeexchange

Population space




01 02 03 10

01 02 03 10

11 12 13 110

F

F

CR

CR

21 22 23 210

01

10

02

03

01

10

02

03

983223 983223 983223

983223 983223 983223

983223 983223 983223

983223 983223 983223








() = 98316310486998520911048699








Mutation strategy

Mutation strategy


02 04 06 08 1

10383891 10383892 10383893 10383894 10383895

04

06

02

10





Δ () (983089983091)








() = 98316310486998520911048699 ()sum () i rand3 lt








and

must be updated too




and are set by

= 1103925min i 1103925min


= 1103925max

i

1103925max

gt or

9830801103925max

983081 gt

otherwise(983089983094)




ollowing equation

11039251103925+11038389 =

983163104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699852091104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699

110392511039251038389 + (0503) lowast 1048616103838911039259073172 1038389 minus 10383891103925


9073173 10383891048617 times rand


907317310383891048617 times rand


9073173 10383891048617 times rand

i 11039251103925

1038389 gt 11039251103925

1038389 gt 11039251103925+11038389 = 983163104869910486998520911048699104869910383891103925


90731711038389 minus lowast 104861610383891103925



(983089983095)



















2

4

7

9

11

13 and


1

sim7 are



6

7 and






Original DE CDEAS

Sphere unction

1





Success rate () 983089983088983088 983089983088983088

imes (s) 983089983096983096983088983091 983089983092983094983088983089983095





Success rate () 983089983088983088 983089983088983088

imes (s) 983090983089983095983096983096 983089983096983089983089983089983095


minus78




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983089983094983092983095 983090983092983089983089983095983096



Mean


18848

times 10

minus28


Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983097983093983094 983090983095983095983088983093983096


Worst 983089983094983094983089983089983093983097 983089983091983097983089983091983093983096

Mean 983095983088983097983091983097983097 983091983097983092983097983091983094

Std 983092983088983088983088983093983090 983091983089983090983096983097983095

Success rate () 983096983094983094983095 983097983094983094983095

imes (s) 983089983097983093983097983092 983089983094983095983090983091983091



398838

times 10

minus49




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983090983089983092983089 983090983092983090983092983090983094


Worst 983088 983088

Mean 983088 983088




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092



Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091


minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089


Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091


Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089


Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095


Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096


Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




Mutation strategy

Mutation strategy


02 04 06 08 1

10383891 10383892 10383893 10383894 10383895

04

06

02

10





Δ () (983089983091)








() = 98316310486998520911048699 ()sum () i rand3 lt








and

must be updated too




and are set by

= 1103925min i 1103925min


= 1103925max

i

1103925max

gt or

9830801103925max

983081 gt

otherwise(983089983094)




ollowing equation

11039251103925+11038389 =

983163104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699852091104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699

110392511039251038389 + (0503) lowast 1048616103838911039259073172 1038389 minus 10383891103925


9073173 10383891048617 times rand


907317310383891048617 times rand


9073173 10383891048617 times rand

i 11039251103925

1038389 gt 11039251103925

1038389 gt 11039251103925+11038389 = 983163104869910486998520911048699104869910383891103925


90731711038389 minus lowast 104861610383891103925



(983089983095)



















2

4

7

9

11

13 and


1

sim7 are



6

7 and






Original DE CDEAS

Sphere unction

1





Success rate () 983089983088983088 983089983088983088

imes (s) 983089983096983096983088983091 983089983092983094983088983089983095





Success rate () 983089983088983088 983089983088983088

imes (s) 983090983089983095983096983096 983089983096983089983089983089983095


minus78




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983089983094983092983095 983090983092983089983089983095983096



Mean


18848

times 10

minus28


Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983097983093983094 983090983095983095983088983093983096


Worst 983089983094983094983089983089983093983097 983089983091983097983089983091983093983096

Mean 983095983088983097983091983097983097 983091983097983092983097983091983094

Std 983092983088983088983088983093983090 983091983089983090983096983097983095

Success rate () 983096983094983094983095 983097983094983094983095

imes (s) 983089983097983093983097983092 983089983094983095983090983091983091



398838

times 10

minus49




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983090983089983092983089 983090983092983090983092983090983094


Worst 983088 983088

Mean 983088 983088




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092



Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091


minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089


Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091


Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089


Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095


Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096


Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




and are set by

= 1103925min i 1103925min


= 1103925max

i

1103925max

gt or

9830801103925max

983081 gt

otherwise(983089983094)




ollowing equation

11039251103925+11038389 =

983163104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699852091104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699104869910486991048699

110392511039251038389 + (0503) lowast 1048616103838911039259073172 1038389 minus 10383891103925


9073173 10383891048617 times rand


907317310383891048617 times rand


9073173 10383891048617 times rand

i 11039251103925

1038389 gt 11039251103925

1038389 gt 11039251103925+11038389 = 983163104869910486998520911048699104869910383891103925


90731711038389 minus lowast 104861610383891103925



(983089983095)



















2

4

7

9

11

13 and


1

sim7 are



6

7 and






Original DE CDEAS

Sphere unction

1





Success rate () 983089983088983088 983089983088983088

imes (s) 983089983096983096983088983091 983089983092983094983088983089983095





Success rate () 983089983088983088 983089983088983088

imes (s) 983090983089983095983096983096 983089983096983089983089983089983095


minus78




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983089983094983092983095 983090983092983089983089983095983096



Mean


18848

times 10

minus28


Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983097983093983094 983090983095983095983088983093983096


Worst 983089983094983094983089983089983093983097 983089983091983097983089983091983093983096

Mean 983095983088983097983091983097983097 983091983097983092983097983091983094

Std 983092983088983088983088983093983090 983091983089983090983096983097983095

Success rate () 983096983094983094983095 983097983094983094983095

imes (s) 983089983097983093983097983092 983089983094983095983090983091983091



398838

times 10

minus49




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983090983089983092983089 983090983092983090983092983090983094


Worst 983088 983088

Mean 983088 983088




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092



Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091


minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089


Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091


Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089


Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095


Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096


Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom





Original DE CDEAS

Sphere unction

1





Success rate () 983089983088983088 983089983088983088

imes (s) 983089983096983096983088983091 983089983092983094983088983089983095





Success rate () 983089983088983088 983089983088983088

imes (s) 983090983089983095983096983096 983089983096983089983089983089983095


minus78




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983089983094983092983095 983090983092983089983089983095983096



Mean


18848

times 10

minus28


Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983097983093983094 983090983095983095983088983093983096


Worst 983089983094983094983089983089983093983097 983089983091983097983089983091983093983096

Mean 983095983088983097983091983097983097 983091983097983092983097983091983094

Std 983092983088983088983088983093983090 983091983089983090983096983097983095

Success rate () 983096983094983094983095 983097983094983094983095

imes (s) 983089983097983093983097983092 983089983094983095983090983091983091



398838

times 10

minus49




Success rate () 983089983088983088 983089983088983088

imes (s) 983091983090983089983092983089 983090983092983090983092983090983094


Worst 983088 983088

Mean 983088 983088




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092



Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091


minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089


Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091


Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089


Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095


Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096


Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983088 983088

Success rate () 983089983088983088 983089983088983088

imes (s) 983091983091983091983095983092



Mean 16332 times 10minus8 983088983089983095983094983091

Std 89457 times 10minus8 983088983092983088983094983096

Success rate () 983089983088983088 983096983091983091983091

imes (s) 983090983092983096983090983088 983090983088983097983091983093983091


minus15

Worst 983088983097983091983089983091 983088983097983091983089983091

Mean 983088983088983091983089983088 983088983088983094983090983088

Std 983088983089983095983088983088

983088983090983091983094983090Success rate () 983097983094983094983095 983097983091983091983091

imes (s) 983090983095983091983091983095 983090983089983094983096983092983089


Worst 983088983088983091983094983095 983088983088983090983095983088

Mean 983088983088983088983090983088 983088983088983088983093983092

Std 983088983088983088983095983092 983088983088983088983095983094

Success rate () 983097983088 983093983094983094983095

imes (s) 983090983093983091983093 983090983088983095983095983097983091


Worst 983088983088983091983089983097

983088983088983091983092983091Mean 983088983088983088983093983094 983088983088983088983094983088

Std 983088983088983088983096983097 983088983088983088983096983096

Success rate () 983096983088 983095983094983094983095

imes (s) 983090983095983095983094983096 983090983090983096983093983092983089


Worst 983091983093983093983096983095983096 983089983090983097983091983092983092

Mean 983090983088983091983093983097983092 983094983093983088983088983091

Std 983094983091983088983095983090 983090983094983094983089983090

Success rate () 983091983091983091 983097983088

imes (s) 983090983095983090983094983092 983090983090983091983090983091983095


Worst 983091983094983097983097983090983091 983094983095983094983093983095

Mean 983089983097983092983095983089983097 983096983090983093983096983089

Std 983096983097983089983094983092 983091983096983094983096983088

Success rate () 983089983094983094983095 983095983094983094983095

imes (s) 983090983097983091983089983091 983090983091983096983096983091983096


Worst 983090983097983097983089983089983090 983089983089983097983096983097983097

Mean 983090983093983092983093983093983094 983096983089983097983092983095




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




983137983138983148983141 983089 Continued

Original DE CDEAS

Std 983090983097983088983095983096 983090983090983092983095983091

Success rate () 983088 983096983094983094983095

imes (s) 983091983089983094983094983091 983090983093983093983091983095983092


15Best 983088 983088

Worst 983089983094 983094

Mean 983094983095983094983094983094 983089983093983091983091983091

Std 983091983092983093983088983097 983089983096983093983089983097

Success rate () 983092983088 983097983094983094983095

imes (s) 983091983091983091983095983092 983090983093983097983092983091983088


Worst 983095983089983088983094983091983088983091 983089983091983094983090983088983093983090983089

Mean 983091983093983095983094983089983095983090983093 983094983095983094983092983089983094983094

Std 983089983092983092983092983089983090983092983092 983091983090983092983090983091983089983095

Success rate () 983097983088 983092983088

imes (s) 983090983093983088983090983096 983089983097983088983088983088983097


Worst 983092983093983089983088983090 983092983095983088983096983094

Mean 983089983089983088983095983095 983089983097983096983092983097

Std 983088983096983094983093983090 983089983089983094983092983089983096

Success rate () 983093983091983091983091 983090983091983091983091

imes (s) 983090983091983096983088983094 983089983097983090983093983088983093


minus45


Mean


26992

times 10

minus43


Success rate () 983089983088983088 983089983088983088

imes (s) 983090983094983090983097983095 983090983088983096983093983095983091


1

3

4

5

6

12

13

14

15 and

18 although










Δ 983080NH3

983081 = NH3OU

minus NH3IN

(983089983096)




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




0 400 800 1200 1600 2000


minus80

minus70

minus60

minus50minus40

minus30

minus20

minus10

0

10

l o g ( 1047297 t n

e s s v a

l u e )


DE and CDEAS for f1

0 400 800 1200 1600 2000


l o g ( 1047297 t n

e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f2

0 400 800 1200 1600 2000


0

minus80

minus70

minus60

minus50

minus40minus30

minus20

minus10

10

l o g ( 1047297 t n e s

s v a

l u e )


DE and CDEAS for f3

0 400 800 1200 1600 2000


10

l o g ( 1047297 t n e s s v a

l u e )

minus30

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f4

1

2

3

4

5

67

8

9

10

11

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f5

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus40

minus45

minus25

minus20

minus15

minus10

minus5

0

5


DE and CDEAS for f6

10

Original DE

CDEAS

0 400 800 1200 1600 2000


l o g ( 1047297 t n e s s v a

l u e )

minus30

minus35

minus25

minus20

minus15

minus10

minus50

5


DE and CDEAS for f7

Original DE

CDEAS

0 400 800 1200 1600 2000


minus16

minus14

minus12

minus10

minus8

minus6

minus4minus2

0

2

l o g ( 1047297 t n e s s v a

l u e )


DE and CDEAS for f8

F983145983143983157983154983141 983094 Continued




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


0 400 800 1200 1600 2000


08

1

12

14

16

182

22

24

26

28

0 400 800 1200 1600 2000


08

1

12

14

16

18

222

24

26

28


08

1

12

14

16

18

222

24

26

28


0

05

1

15

2

25

3


Original DE

CDEAS

22

24

26

28

3

32

34

3638

4

42


Original DE

CDEAS

0

2

minus16

minus14

minus12

minus10

minus8

minus6

minus4

minus2 0

2

4

minus16

minus14

minus12

minus10

minus8minus6

minus4

minus2

0

1

2

3

minus3

minus2

minus1


DE and CDEAS for f9















l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s v a

l u e )

l o g ( 1047297 t n e s s

v a

l u e )

l o g ( f t n e s s

v a

l u e )



l u e )



l u e )

F983145983143983157983154983141 983094 Continued











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom











minus04


raining error 983088983088983088983090983090983091983089









minus04

















Appendix


1

(1103925) =

991761=111039252



2 (1103925) = 991761=1

2 = 1103925 minus

= 9831311

2


(A983090)




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




0 50 100 150 200 2500106

0107

0108

0109

011

0111

0112

0113

0114

0115

0116

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 10 20 30 40 50 60 70 80 900105

0106

0107

0108

0109

011

0111

0112

0113

0114

0115

Sample number

N e t v a

l u e o

a m m o n i a ( )

0 50 100 150 200 250

Sample number

N e t v a


0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a


Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

0110111

0112

0113

0114

0115

0 50 100 150 200 250

Sample number

N e t v a

l u e o

a

m m o n i a ( )

0106

0107

0108

0109

0110111

0112

0113

0114

0115

0116

N e t v a

l u e o

a

m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115

N e t v a

l u e o

a m m o n i a ( )

Sample number

0 50 100 150 200 2500106

0107

0108

0109

0110111

0112

0113

0114

0115

0116


N e t v a

l u e o

a m m o n i a ( )

Sample number

0 10 20 30 40 50 60 70 80 900107

0108

0109

011

0111

0112

0113

0114

0115








983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom






983091983088


3 983088 983088

[minus100100]

10minus5

4 983088 [minus100100]

10minus5


15

983088

[minus55] 983093

16 983092983089983096983097983096983090983097 983088 [minus500500]



3 (1103925) = 991761=1

991761=1

11039252


(A983091)


4 (1103925) = 991761=1

991761=1

2 = 1103925 minus






6 (1103925) = 991761=1

991761=1

11039252 lowast (1 + 04 | (0 1)|)


(A983094)


7 (1103925) = 991761=1

991761=1

2 lowast (1 + 04 | (0 1)|)




11039252minus exp 1 991761

=1

cos 98308021103925983081 + 20 +


(A983096)




=1

cos 9830802983081 + 20 + = 1103925 minus

= 9831311

2


(A983097)





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom





10 (1103925) = 991761=1

110392524000 minus prod=1

cos 1103925991770 + 1


(A983089983088)


11 (1103925) = 991761=1

24000 minus prod=1

cos 991770 + 1


(A983089983089)


12 (1103925) =

991761=1 104861611039252

minus 10cos



13 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 1103925 minus



14 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699


(A983089983092)


15 (1103925) = 991761=1

10486162 minus 10 cos 9830802983081 + 101048617 = 98316310486998520911048699

lt 12round 98308029830812 ge 12 or = 1 2


(A983089983093)


16 (1103925) = 4189829 times minus 991761=1

1103925 sin 110392512




17 (1103925) = 991761=1

1103925 + prod=1



Acknowledgments


References



























httpwwwhindawicom




















httpwwwhindawicom

ammonia reactor design

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